def _setup_facet_dofs(self, dim, facet_desc, facet_perms, offset):
"""
Helper function to setup facet DOF connectivity, works for both
edges and faces.
"""
facet_desc = nm.array(facet_desc)
n_dof_per_facet = facet_desc.shape[1]
cmesh = self.domain.cmesh
facets = self.region.entities[dim]
ii = nm.arange(facets.shape[0], dtype=nm.int32)
all_dofs = offset + expand_nodes_to_dofs(ii, n_dof_per_facet)
# Prepare global facet id remapping to field-local numbering.
remap = prepare_remap(facets, cmesh.num[dim])
cconn = self.region.domain.cmesh.get_conn(self.region.tdim, dim)
offs = cconn.offsets
n_f = self.gel.edges.shape[0] if dim == 1 else self.gel.faces.shape[0]
oris = cmesh.get_orientations(dim)
for ig, ap in self.aps.iteritems():
gcells = self.region.get_cells(ig, offset=False)
n_el = gcells.shape[0]
indices = cconn.indices[offs[gcells[0]]:offs[gcells[-1]+1]]
facets_of_cells = remap[indices]
ori = oris[offs[gcells[0]]:offs[gcells[-1]+1]]
perms = facet_perms[ig][ori]
# Define global facet dof numbers.
gdofs = offset + expand_nodes_to_dofs(facets_of_cells,
n_dof_per_facet)
# Elements of facets.
iel = nm.arange(n_el, dtype=nm.int32).repeat(n_f)
ies = nm.tile(nm.arange(n_f, dtype=nm.int32), n_el)
# DOF columns in econn for each facet.
iep = facet_desc[ies]
iaux = nm.arange(gdofs.shape[0], dtype=nm.int32)
ap.econn[iel[:, None], iep] = gdofs[iaux[:, None], perms]
n_dof = n_dof_per_facet * facets.shape[0]
assert_(n_dof == nm.prod(all_dofs.shape))
return n_dof, all_dofs, remap
def _setup_facet_dofs(self, dim, facet_desc, facet_perms, offset):
"""
Helper function to setup facet DOF connectivity, works for both
edges and faces.
"""
facet_desc = nm.array(facet_desc)
n_dof_per_facet = facet_desc.shape[1]
cmesh = self.domain.cmesh
facets = self.region.entities[dim]
ii = nm.arange(facets.shape[0], dtype=nm.int32)
all_dofs = offset + expand_nodes_to_dofs(ii, n_dof_per_facet)
# Prepare global facet id remapping to field-local numbering.
remap = prepare_remap(facets, cmesh.num[dim])
cconn = self.region.domain.cmesh.get_conn(self.region.tdim, dim)
offs = cconn.offsets
n_f = self.gel.edges.shape[0] if dim == 1 else self.gel.faces.shape[0]
oris = cmesh.get_orientations(dim)
for ig, ap in self.aps.iteritems():
gcells = self.region.get_cells(ig, offset=False)
n_el = gcells.shape[0]
indices = cconn.indices[offs[gcells[0]]:offs[gcells[-1] + 1]]
facets_of_cells = remap[indices]
ori = oris[offs[gcells[0]]:offs[gcells[-1] + 1]]
perms = facet_perms[ig][ori]
# Define global facet dof numbers.
gdofs = offset + expand_nodes_to_dofs(facets_of_cells,
n_dof_per_facet)
# Elements of facets.
iel = nm.arange(n_el, dtype=nm.int32).repeat(n_f)
ies = nm.tile(nm.arange(n_f, dtype=nm.int32), n_el)
# DOF columns in econn for each facet.
iep = facet_desc[ies]
iaux = nm.arange(gdofs.shape[0], dtype=nm.int32)
ap.econn[iel[:, None], iep] = gdofs[iaux[:, None], perms]
n_dof = n_dof_per_facet * facets.shape[0]
assert_(n_dof == nm.prod(all_dofs.shape))
return n_dof, all_dofs, remap
def _setup_facet_dofs(self, facets, facet_desc, facet_perms,
get_facets, offset):
"""
Helper function to setup facet DOF connectivity, works for both
edges and faces.
"""
facet_desc = nm.array(facet_desc)
n_dof_per_facet = facet_desc.shape[1]
# Prepare global facet id remapping to field-local numbering.
uids = []
for ig, ap in self.aps.iteritems():
ii = get_facets(ig)
uid_i = facets.uid_i[ii]
uids.append(uid_i)
uids = nm.unique(nm.concatenate(uids))
n_uid = uids.shape[0]
lids = nm.arange(n_uid, dtype=nm.int32)
remap = prepare_remap(uids, facets.n_unique)
all_dofs = offset + expand_nodes_to_dofs(lids, n_dof_per_facet)
for ig, ap in self.aps.iteritems():
ori = facets.oris[ig]
perms = facet_perms[ig][ori]
ii = get_facets(ig)
g_uid = facets.uid_i[ii]
uid = remap[g_uid]
# Define global facet dof numbers.
gdofs = offset + expand_nodes_to_dofs(uid, n_dof_per_facet)
# Elements of facets.
iel = facets.indices[ii, 1]
ies = facets.indices[ii, 2]
# DOF columns in econn for each facet.
iep = facet_desc[ies]
iaux = nm.arange(gdofs.shape[0], dtype=nm.int32)
ap.econn[iel[:, None], iep] = gdofs[iaux[:, None], perms]
n_dof = n_dof_per_facet * n_uid
assert_(n_dof == nm.prod(all_dofs.shape))
return n_dof, all_dofs, remap
def _setup_facet_dofs(self, facets, facet_desc, get_facets, offset):
"""
Helper function to setup facet DOF connectivity, works for both
edges and faces.
"""
facet_desc = nm.array(facet_desc)
n_dof_per_facet = facet_desc.shape[1]
# Prepare global facet id remapping to field-local numbering.
uids = []
for ig, ap in self.aps.iteritems():
ii = get_facets(ig)
uid_i = facets.uid_i[ii]
uids.append(uid_i)
uids = nm.unique(nm.concatenate(uids))
n_uid = uids.shape[0]
lids = nm.arange(n_uid, dtype=nm.int32)
remap = prepare_remap(uids, facets.n_unique)
all_dofs = offset + expand_nodes_to_dofs(lids, n_dof_per_facet)
for ig, ap in self.aps.iteritems():
n_fp = facets.n_fps[ig]
if (n_fp == 2) and (ap.interp.gel.name in ['2_4', '3_8']):
tp_edges = ap.interp.gel.edges
ecs = ap.interp.gel.coors[tp_edges]
# True = positive, False = negative edge orientation w.r.t.
# reference tensor product axes.
tp_edge_ori = (nm.diff(ecs, axis=1).sum(axis=2) > 0).squeeze()
else:
tp_edge_ori = None
ori = facets.get_orientation(ig, tp_edge_ori)
ii = get_facets(ig)
g_uid = facets.uid_i[ii]
uid = remap[g_uid]
# Define global facet dof numbers.
gdofs = offset + expand_nodes_to_dofs(uid, n_dof_per_facet)
# Elements of facets.
iel = facets.indices[ii, 1]
ies = facets.indices[ii, 2]
# DOF columns in econn for each facet (repeating same values for
# each element.
iep = facet_desc[ies]
ap.econn[iel[:, None], iep] = gdofs
if n_fp == 2: # Edges.
# ori == 1 means the basis has to be multiplied by -1.
ps = ap.interp.poly_spaces['v']
orders = ps.node_orders
eori = nm.repeat(ori[:, None], n_dof_per_facet, 1)
eoo = orders[iep] % 2 # Odd orders.
ap.ori[iel[:, None], iep] = eori * eoo
elif n_fp == 3: # Triangular faces.
raise NotImplementedError
else: # Quadrilateral faces.
# ori encoding in 3 bits:
# 0: axis swap, 1: axis 1 sign, 2: axis 2 sign
# 0 = + or False, 1 = - or True
# 63 -> 000 = 0
# 0 -> 001 = 1
# 30 -> 010 = 2
# 33 -> 011 = 3
# 11 -> 100 = 4
# 7 -> 101 = 5
# 52 -> 110 = 6
# 56 -> 111 = 7
# Special cases:
# Both orders same and even -> 000
# Both orders same and odd -> 0??
# Bits 1, 2 are multiplied by (swapped) axial order % 2.
new = nm.repeat(nm.arange(8, dtype=nm.int32), 3)
translate = prepare_translate([31, 59, 63,
0, 1, 4,
22, 30, 62,
32, 33, 41,
11, 15, 43,
3, 6, 7,
20, 52, 60,
48, 56, 57], new)
ori = translate[ori]
eori = nm.repeat(ori[:, None], n_dof_per_facet, 1)
ps = ap.interp.poly_spaces['v']
orders = ps.face_axes_nodes[iep - ps.face_indx[0]]
eoo = orders % 2
eoo0, eoo1 = eoo[..., 0], eoo[..., 1]
i0 = nm.where(eori < 4)
i1 = nm.where(eori >= 4)
eori[i0] = nm.bitwise_and(eori[i0], 2*eoo0[i0] + 5)
eori[i0] = nm.bitwise_and(eori[i0], eoo1[i0] + 6)
eori[i1] = nm.bitwise_and(eori[i1], eoo0[i1] + 6)
eori[i1] = nm.bitwise_and(eori[i1], 2*eoo1[i1] + 5)
ap.ori[iel[:, None], iep] = eori
n_dof = n_dof_per_facet * n_uid
assert_(n_dof == nm.prod(all_dofs.shape))
return n_dof, all_dofs, remap
def _setup_facet_dofs(self, dim, facet_desc, get_facets, offset):
"""
Helper function to setup facet DOF connectivity, works for both
edges and faces.
"""
facet_desc = nm.array(facet_desc)
n_dof_per_facet = facet_desc.shape[1]
cmesh = self.domain.cmesh
facets = self.region.entities[dim]
ii = nm.arange(facets.shape[0], dtype=nm.int32)
all_dofs = offset + expand_nodes_to_dofs(ii, n_dof_per_facet)
# Prepare global facet id remapping to field-local numbering.
remap = prepare_remap(facets, cmesh.num[dim])
cconn = self.region.domain.cmesh.get_conn(self.region.tdim, dim)
offs = cconn.offsets
n_f = self.gel.edges.shape[0] if dim == 1 else self.gel.faces.shape[0]
n_fp = 2 if dim == 1 else self.gel.surface_facet.n_vertex
oris = cmesh.get_orientations(dim)
for ig, ap in self.aps.iteritems():
gcells = self.region.get_cells(ig, offset=False)
n_el = gcells.shape[0]
indices = cconn.indices[offs[gcells[0]] : offs[gcells[-1] + 1]]
facets_of_cells = remap[indices]
# Define global facet dof numbers.
gdofs = offset + expand_nodes_to_dofs(facets_of_cells, n_dof_per_facet)
# Elements of facets.
iel = nm.arange(n_el, dtype=nm.int32).repeat(n_f)
ies = nm.tile(nm.arange(n_f, dtype=nm.int32), n_el)
# DOF columns in econn for each facet (repeating same values for
# each element.
iep = facet_desc[ies]
ap.econn[iel[:, None], iep] = gdofs
ori = oris[offs[gcells[0]] : offs[gcells[-1] + 1]]
if (n_fp == 2) and (ap.interp.gel.name in ["2_4", "3_8"]):
tp_edges = ap.interp.gel.edges
ecs = ap.interp.gel.coors[tp_edges]
# True = positive, False = negative edge orientation w.r.t.
# reference tensor product axes.
tp_edge_ori = (nm.diff(ecs, axis=1).sum(axis=2) > 0).squeeze()
aux = nm.tile(tp_edge_ori, n_el)
ori = nm.where(aux, ori, 1 - ori)
if n_fp == 2: # Edges.
# ori == 1 means the basis has to be multiplied by -1.
ps = ap.interp.poly_spaces["v"]
orders = ps.node_orders
eori = nm.repeat(ori[:, None], n_dof_per_facet, 1)
eoo = orders[iep] % 2 # Odd orders.
ap.ori[iel[:, None], iep] = eori * eoo
elif n_fp == 3: # Triangular faces.
raise NotImplementedError
else: # Quadrilateral faces.
# ori encoding in 3 bits:
# 0: axis swap, 1: axis 1 sign, 2: axis 2 sign
# 0 = + or False, 1 = - or True
# 63 -> 000 = 0
# 0 -> 001 = 1
# 30 -> 010 = 2
# 33 -> 011 = 3
# 11 -> 100 = 4
# 7 -> 101 = 5
# 52 -> 110 = 6
# 56 -> 111 = 7
# Special cases:
# Both orders same and even -> 000
# Both orders same and odd -> 0??
# Bits 1, 2 are multiplied by (swapped) axial order % 2.
new = nm.repeat(nm.arange(8, dtype=nm.int32), 3)
translate = prepare_translate(
[31, 59, 63, 0, 1, 4, 22, 30, 62, 32, 33, 41, 11, 15, 43, 3, 6, 7, 20, 52, 60, 48, 56, 57], new
)
ori = translate[ori]
eori = nm.repeat(ori[:, None], n_dof_per_facet, 1)
ps = ap.interp.poly_spaces["v"]
orders = ps.face_axes_nodes[iep - ps.face_indx[0]]
eoo = orders % 2
eoo0, eoo1 = eoo[..., 0], eoo[..., 1]
i0 = nm.where(eori < 4)
i1 = nm.where(eori >= 4)
eori[i0] = nm.bitwise_and(eori[i0], 2 * eoo0[i0] + 5)
eori[i0] = nm.bitwise_and(eori[i0], eoo1[i0] + 6)
eori[i1] = nm.bitwise_and(eori[i1], eoo0[i1] + 6)
eori[i1] = nm.bitwise_and(eori[i1], 2 * eoo1[i1] + 5)
ap.ori[iel[:, None], iep] = eori
n_dof = n_dof_per_facet * facets.shape[0]
assert_(n_dof == nm.prod(all_dofs.shape))
return n_dof, all_dofs, remap